plutarch-1.10.1
Safe HaskellSafe-Inferred
LanguageGHC2021

Plutarch.Internal.Numeric

Synopsis

Types

data PPositive (s :: S) Source #

Since: 1.10.0

Instances

Instances details
PCountable PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Enum

Methods

psuccessor :: forall (s :: S). Term s (PPositive :--> PPositive) Source #

psuccessorN :: forall (s :: S). Term s (PPositive :--> (PPositive :--> PPositive)) Source #

PEq PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#==) :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PBool Source #

PIsData PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pfromDataImpl :: forall (s :: S). Term s (PAsData PPositive) -> Term s PPositive Source #

pdataImpl :: forall (s :: S). Term s PPositive -> Term s PData Source #

PLiftable PPositive Source # 
Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type AsHaskell PPositive Source #

type PlutusRepr PPositive Source #

Methods

haskToRepr :: AsHaskell PPositive -> PlutusRepr PPositive Source #

reprToHask :: PlutusRepr PPositive -> Either LiftError (AsHaskell PPositive) Source #

reprToPlut :: forall (s :: S). PlutusRepr PPositive -> PLifted s PPositive Source #

plutToRepr :: (forall (s :: S). PLifted s PPositive) -> Either LiftError (PlutusRepr PPositive) Source #

PAdditiveSemigroup PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#+) :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

pscalePositive :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

PMultiplicativeMonoid PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pone :: forall (s :: S). Term s PPositive Source #

ppowNatural :: forall (s :: S). Term s PPositive -> Term s PNatural -> Term s PPositive Source #

PMultiplicativeSemigroup PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#*) :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

ppowPositive :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

POrd PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#<=) :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PBool Source #

(#<) :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PBool Source #

pmax :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

pmin :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

PlutusType PPositive Source # 
Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type PInner PPositive :: PType Source #

type PCovariant' PPositive Source #

type PContravariant' PPositive Source #

type PVariant' PPositive Source #

Methods

pcon' :: forall (s :: S). PPositive s -> Term s (PInner PPositive) Source #

pmatch' :: forall (s :: S) (b :: PType). Term s (PInner PPositive) -> (PPositive s -> Term s b) -> Term s b Source #

PShow PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Show

Methods

pshow' :: forall (s :: S). Bool -> Term s PPositive -> Term s PString Source #

PTryFrom PInteger PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.TryFrom

Associated Types

type PTryFromExcess PInteger PPositive :: PType Source #

Methods

ptryFrom' :: forall (s :: S) (r :: PType). Term s PInteger -> ((Term s PPositive, Reduce (PTryFromExcess PInteger PPositive s)) -> Term s r) -> Term s r Source #

PTryFrom PData (PAsData PPositive) Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.TryFrom

Associated Types

type PTryFromExcess PData (PAsData PPositive) :: PType Source #

Methods

ptryFrom' :: forall (s :: S) (r :: PType). Term s PData -> ((Term s (PAsData PPositive), Reduce (PTryFromExcess PData (PAsData PPositive) s)) -> Term s r) -> Term s r Source #

Generic (PPositive s) Source # 
Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type Rep (PPositive s) :: Type -> Type Source #

Methods

from :: PPositive s -> Rep (PPositive s) x Source #

to :: Rep (PPositive s) x -> PPositive s Source #

Generic (PPositive s) Source # 
Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type Code (PPositive s) :: [[Type]]

Methods

from :: PPositive s -> Rep (PPositive s)

to :: Rep (PPositive s) -> PPositive s

type AsHaskell PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type AsHaskell PPositive = AsHaskell (DeriveNewtypePLiftable PPositive Positive)
type PlutusRepr PPositive Source # 
Instance details

Defined in Plutarch.Internal.Numeric

type PlutusRepr PPositive = PlutusRepr (DeriveNewtypePLiftable PPositive Positive)
type PContravariant' PPositive Source # 
Instance details

Defined in Plutarch.Internal.Numeric

type PContravariant' PPositive = PContravariant' (DeriveNewtypePlutusType PPositive)
type PCovariant' PPositive Source # 
Instance details

Defined in Plutarch.Internal.Numeric

type PCovariant' PPositive = PCovariant' (DeriveNewtypePlutusType PPositive)
type PInner PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type PInner PPositive = PInner (DeriveNewtypePlutusType PPositive)
type PVariant' PPositive Source # 
Instance details

Defined in Plutarch.Internal.Numeric

type PVariant' PPositive = PVariant' (DeriveNewtypePlutusType PPositive)
type PTryFromExcess PInteger PPositive Source # 
Instance details

Defined in Plutarch.Internal.TryFrom

type PTryFromExcess PInteger PPositive = Const () :: S -> Type
type PTryFromExcess PData (PAsData PPositive) Source # 
Instance details

Defined in Plutarch.Internal.TryFrom

type PTryFromExcess PData (PAsData PPositive)
type Rep (PPositive s) Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type Rep (PPositive s) = D1 ('MetaData "PPositive" "Plutarch.Internal.Numeric" "plutarch-1.10.1-LPGZaAWjybFFuyJX8dF1yJ" 'True) (C1 ('MetaCons "PPositive" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Term s PInteger))))
type Code (PPositive s) Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type Code (PPositive s) = GCode (PPositive s)

data Positive Source #

Since: 1.10.0

Instances

Instances details
Arbitrary Positive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

arbitrary :: Gen Positive

shrink :: Positive -> [Positive]

CoArbitrary Positive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

coarbitrary :: Positive -> Gen b -> Gen b

Function Positive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

function :: (Positive -> b) -> Positive :-> b

Show Positive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

showsPrec :: Int -> Positive -> ShowS Source #

show :: Positive -> String Source #

showList :: [Positive] -> ShowS Source #

Eq Positive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(==) :: Positive -> Positive -> Bool Source #

(/=) :: Positive -> Positive -> Bool Source #

Ord Positive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

compare :: Positive -> Positive -> Ordering Source #

(<) :: Positive -> Positive -> Bool Source #

(<=) :: Positive -> Positive -> Bool Source #

(>) :: Positive -> Positive -> Bool Source #

(>=) :: Positive -> Positive -> Bool Source #

max :: Positive -> Positive -> Positive Source #

min :: Positive -> Positive -> Positive Source #

Pretty Positive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pretty :: Positive -> Doc ann

prettyList :: [Positive] -> Doc ann

data PNatural (s :: S) Source #

Since: 1.10.0

Instances

Instances details
PEq PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#==) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PBool Source #

PIsData PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pfromDataImpl :: forall (s :: S). Term s (PAsData PNatural) -> Term s PNatural Source #

pdataImpl :: forall (s :: S). Term s PNatural -> Term s PData Source #

PLiftable PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type AsHaskell PNatural Source #

type PlutusRepr PNatural Source #

Methods

haskToRepr :: AsHaskell PNatural -> PlutusRepr PNatural Source #

reprToHask :: PlutusRepr PNatural -> Either LiftError (AsHaskell PNatural) Source #

reprToPlut :: forall (s :: S). PlutusRepr PNatural -> PLifted s PNatural Source #

plutToRepr :: (forall (s :: S). PLifted s PNatural) -> Either LiftError (PlutusRepr PNatural) Source #

PAdditiveMonoid PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pzero :: forall (s :: S). Term s PNatural Source #

pscaleNatural :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

PAdditiveSemigroup PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#+) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

pscalePositive :: forall (s :: S). Term s PNatural -> Term s PPositive -> Term s PNatural Source #

PMultiplicativeMonoid PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pone :: forall (s :: S). Term s PNatural Source #

ppowNatural :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

PMultiplicativeSemigroup PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#*) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

ppowPositive :: forall (s :: S). Term s PNatural -> Term s PPositive -> Term s PNatural Source #

POrd PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#<=) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PBool Source #

(#<) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PBool Source #

pmax :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

pmin :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

PlutusType PNatural Source # 
Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type PInner PNatural :: PType Source #

type PCovariant' PNatural Source #

type PContravariant' PNatural Source #

type PVariant' PNatural Source #

Methods

pcon' :: forall (s :: S). PNatural s -> Term s (PInner PNatural) Source #

pmatch' :: forall (s :: S) (b :: PType). Term s (PInner PNatural) -> (PNatural s -> Term s b) -> Term s b Source #

Generic (PNatural s) Source # 
Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type Rep (PNatural s) :: Type -> Type Source #

Methods

from :: PNatural s -> Rep (PNatural s) x Source #

to :: Rep (PNatural s) x -> PNatural s Source #

Generic (PNatural s) Source # 
Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type Code (PNatural s) :: [[Type]]

Methods

from :: PNatural s -> Rep (PNatural s)

to :: Rep (PNatural s) -> PNatural s

type AsHaskell PNatural Source # 
Instance details

Defined in Plutarch.Internal.Numeric

type AsHaskell PNatural = Natural
type PlutusRepr PNatural Source # 
Instance details

Defined in Plutarch.Internal.Numeric

type PlutusRepr PNatural = Integer
type PContravariant' PNatural Source # 
Instance details

Defined in Plutarch.Internal.Numeric

type PContravariant' PNatural = PContravariant' (DeriveNewtypePlutusType PNatural)
type PCovariant' PNatural Source # 
Instance details

Defined in Plutarch.Internal.Numeric

type PCovariant' PNatural = PCovariant' (DeriveNewtypePlutusType PNatural)
type PInner PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type PInner PNatural = PInner (DeriveNewtypePlutusType PNatural)
type PVariant' PNatural Source # 
Instance details

Defined in Plutarch.Internal.Numeric

type PVariant' PNatural = PVariant' (DeriveNewtypePlutusType PNatural)
type Rep (PNatural s) Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type Rep (PNatural s) = D1 ('MetaData "PNatural" "Plutarch.Internal.Numeric" "plutarch-1.10.1-LPGZaAWjybFFuyJX8dF1yJ" 'True) (C1 ('MetaCons "PNatural" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Term s PInteger))))
type Code (PNatural s) Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type Code (PNatural s) = GCode (PNatural s)

Type classes

class PAdditiveSemigroup (a :: S -> Type) where Source #

The addition operation, and the notion of scaling by a positive.

Laws

  1. x #+ y = y #+ x (commutativity of #+)
  2. x #+ (y #+ z) = (x #+ y) #+ z (associativity of #+)

If you define a custom pscalePositive, ensure the following also hold:

  1. pscalePositive x pone = x
  2. (pscalePositive x n) #+ (pscalePositive x m) = pscalePositive x (n #+ m)
  3. pscalePositive (pscalePositive x n) m = pscalePositive x (n #* m)

The default implementation ensures these laws are satisfied.

Since: 1.10.0

Minimal complete definition

Nothing

Methods

(#+) :: forall (s :: S). Term s a -> Term s a -> Term s a infix 6 Source #

default (#+) :: forall (s :: S). PAdditiveSemigroup (PInner a) => Term s a -> Term s a -> Term s a Source #

pscalePositive :: forall (s :: S). Term s a -> Term s PPositive -> Term s a Source #

This defaults to exponentiation-by-squaring, which in general is the best we can do.

Instances

Instances details
PAdditiveSemigroup PBuiltinBLS12_381_G1_Element Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#+) :: forall (s :: S). Term s PBuiltinBLS12_381_G1_Element -> Term s PBuiltinBLS12_381_G1_Element -> Term s PBuiltinBLS12_381_G1_Element Source #

pscalePositive :: forall (s :: S). Term s PBuiltinBLS12_381_G1_Element -> Term s PPositive -> Term s PBuiltinBLS12_381_G1_Element Source #

PAdditiveSemigroup PBuiltinBLS12_381_G2_Element Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#+) :: forall (s :: S). Term s PBuiltinBLS12_381_G2_Element -> Term s PBuiltinBLS12_381_G2_Element -> Term s PBuiltinBLS12_381_G2_Element Source #

pscalePositive :: forall (s :: S). Term s PBuiltinBLS12_381_G2_Element -> Term s PPositive -> Term s PBuiltinBLS12_381_G2_Element Source #

PAdditiveSemigroup PInteger Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#+) :: forall (s :: S). Term s PInteger -> Term s PInteger -> Term s PInteger Source #

pscalePositive :: forall (s :: S). Term s PInteger -> Term s PPositive -> Term s PInteger Source #

PAdditiveSemigroup PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#+) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

pscalePositive :: forall (s :: S). Term s PNatural -> Term s PPositive -> Term s PNatural Source #

PAdditiveSemigroup PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#+) :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

pscalePositive :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

PAdditiveSemigroup PRational Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Rational

Methods

(#+) :: forall (s :: S). Term s PRational -> Term s PRational -> Term s PRational Source #

pscalePositive :: forall (s :: S). Term s PRational -> Term s PPositive -> Term s PRational Source #

class PAdditiveSemigroup a => PAdditiveMonoid (a :: S -> Type) where Source #

The notion of zero, as well as a way to scale by naturals.

Laws

  1. pzero #+ x = x (pzero is the identity of #+)
  2. pscalePositive pzero n = pzero (pzero does not scale up)

If you define pscaleNatural, ensure the following as well:

  1. pscaleNatural x (ppositiveToNatural # p) = pscalePositive x p
  2. pscaleNatural x pzero = pzero

The default implementation of pscaleNatural ensures these laws hold.

Since: 1.10.0

Minimal complete definition

pzero

Methods

pzero :: forall (s :: S). Term s a Source #

pscaleNatural :: forall (s :: S). Term s a -> Term s PNatural -> Term s a Source #

Instances

Instances details
PAdditiveMonoid PBuiltinBLS12_381_G1_Element Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pzero :: forall (s :: S). Term s PBuiltinBLS12_381_G1_Element Source #

pscaleNatural :: forall (s :: S). Term s PBuiltinBLS12_381_G1_Element -> Term s PNatural -> Term s PBuiltinBLS12_381_G1_Element Source #

PAdditiveMonoid PBuiltinBLS12_381_G2_Element Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pzero :: forall (s :: S). Term s PBuiltinBLS12_381_G2_Element Source #

pscaleNatural :: forall (s :: S). Term s PBuiltinBLS12_381_G2_Element -> Term s PNatural -> Term s PBuiltinBLS12_381_G2_Element Source #

PAdditiveMonoid PInteger Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pzero :: forall (s :: S). Term s PInteger Source #

pscaleNatural :: forall (s :: S). Term s PInteger -> Term s PNatural -> Term s PInteger Source #

PAdditiveMonoid PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pzero :: forall (s :: S). Term s PNatural Source #

pscaleNatural :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

PAdditiveMonoid PRational Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Rational

Methods

pzero :: forall (s :: S). Term s PRational Source #

pscaleNatural :: forall (s :: S). Term s PRational -> Term s PNatural -> Term s PRational Source #

class PAdditiveMonoid a => PAdditiveGroup (a :: S -> Type) where Source #

The notion of additive inverses, and the subtraction operation.

Laws

If you define pnegate, the following laws must hold:

  1. (pnegate # x) #+ x = pzero (pnegate is an additive inverse)
  2. pnegate #$ pnegate # x = x (pnegate is self-inverting)

If you define #-, the following law must hold:

  1. x #- x = pzero

Additionally, the following 'consistency laws' must hold. Default implementations of both pnegate and #- uphold these.

  1. pnegate # x = pzero #- x
  2. x #- y = x #+ (pnegate # y)

Lastly, if you define a custom pscaleInteger, the following laws must hold:

  1. pscaleInteger x pzero = pzero
  2. pscaleInteger x (pnegate # y) = pnegate # (pscaleInteger x y)

Since: 1.10.0

Minimal complete definition

pnegate | (#-)

Methods

pnegate :: forall (s :: S). Term s (a :--> a) Source #

(#-) :: forall (s :: S). Term s a -> Term s a -> Term s a infix 6 Source #

pscaleInteger :: forall (s :: S). Term s a -> Term s PInteger -> Term s a Source #

Instances

Instances details
PAdditiveGroup PBuiltinBLS12_381_G1_Element Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pnegate :: forall (s :: S). Term s (PBuiltinBLS12_381_G1_Element :--> PBuiltinBLS12_381_G1_Element) Source #

(#-) :: forall (s :: S). Term s PBuiltinBLS12_381_G1_Element -> Term s PBuiltinBLS12_381_G1_Element -> Term s PBuiltinBLS12_381_G1_Element Source #

pscaleInteger :: forall (s :: S). Term s PBuiltinBLS12_381_G1_Element -> Term s PInteger -> Term s PBuiltinBLS12_381_G1_Element Source #

PAdditiveGroup PBuiltinBLS12_381_G2_Element Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pnegate :: forall (s :: S). Term s (PBuiltinBLS12_381_G2_Element :--> PBuiltinBLS12_381_G2_Element) Source #

(#-) :: forall (s :: S). Term s PBuiltinBLS12_381_G2_Element -> Term s PBuiltinBLS12_381_G2_Element -> Term s PBuiltinBLS12_381_G2_Element Source #

pscaleInteger :: forall (s :: S). Term s PBuiltinBLS12_381_G2_Element -> Term s PInteger -> Term s PBuiltinBLS12_381_G2_Element Source #

PAdditiveGroup PInteger Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pnegate :: forall (s :: S). Term s (PInteger :--> PInteger) Source #

(#-) :: forall (s :: S). Term s PInteger -> Term s PInteger -> Term s PInteger Source #

pscaleInteger :: forall (s :: S). Term s PInteger -> Term s PInteger -> Term s PInteger Source #

PAdditiveGroup PRational Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Rational

Methods

pnegate :: forall (s :: S). Term s (PRational :--> PRational) Source #

(#-) :: forall (s :: S). Term s PRational -> Term s PRational -> Term s PRational Source #

pscaleInteger :: forall (s :: S). Term s PRational -> Term s PInteger -> Term s PRational Source #

class PMultiplicativeSemigroup (a :: S -> Type) where Source #

The multiplication operation.

Laws

  1. x #* (y #* z) = (x #* y) #* z (associativity of #*)

If you define a custom ppowPositive, ensure the following also hold:

  1. ppowPositive x pone = x
  2. (ppowPositive x n) #* (ppowPositive x m) = ppowPositive x (n #+ m)
  3. ppowPositive (ppowPositive x n) m = ppowPositive x (n #* m)

The default implementation ensures these laws are satisfied.

Note

Unlike PAdditiveSemigroup, the multiplication operation doesn't need to be commutative. Currently, all Plutarch-provided instances are, but this need not be true for other instances.

Since: 1.10.0

Minimal complete definition

Nothing

Methods

(#*) :: forall (s :: S). Term s a -> Term s a -> Term s a infix 6 Source #

default (#*) :: forall (s :: S). PMultiplicativeSemigroup (PInner a) => Term s a -> Term s a -> Term s a Source #

ppowPositive :: forall (s :: S). Term s a -> Term s PPositive -> Term s a Source #

Instances

Instances details
PMultiplicativeSemigroup PBuiltinBLS12_381_MlResult Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#*) :: forall (s :: S). Term s PBuiltinBLS12_381_MlResult -> Term s PBuiltinBLS12_381_MlResult -> Term s PBuiltinBLS12_381_MlResult Source #

ppowPositive :: forall (s :: S). Term s PBuiltinBLS12_381_MlResult -> Term s PPositive -> Term s PBuiltinBLS12_381_MlResult Source #

PMultiplicativeSemigroup PInteger Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#*) :: forall (s :: S). Term s PInteger -> Term s PInteger -> Term s PInteger Source #

ppowPositive :: forall (s :: S). Term s PInteger -> Term s PPositive -> Term s PInteger Source #

PMultiplicativeSemigroup PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#*) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

ppowPositive :: forall (s :: S). Term s PNatural -> Term s PPositive -> Term s PNatural Source #

PMultiplicativeSemigroup PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#*) :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

ppowPositive :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

PMultiplicativeSemigroup PRational Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Rational

Methods

(#*) :: forall (s :: S). Term s PRational -> Term s PRational -> Term s PRational Source #

ppowPositive :: forall (s :: S). Term s PRational -> Term s PPositive -> Term s PRational Source #

class PMultiplicativeSemigroup a => PMultiplicativeMonoid (a :: S -> Type) where Source #

The notion of one (multiplicative identity), and exponentiation by - naturals.

Laws

  1. pone #* x = x (pone is the left identity of #*)
  2. x #* pone = x (pone is the right identity of #*)
  3. ppowPositive pone p = pone (pone does not scale up)

If you define ppowNatural, ensure the following as well:

  1. ppowNatural x (ppositiveToNatural # p) = ppowPositive x p
  2. ppowNatural x pzero = pone

Since: 1.10.0

Minimal complete definition

pone

Methods

pone :: forall (s :: S). Term s a Source #

ppowNatural :: forall (s :: S). Term s a -> Term s PNatural -> Term s a Source #

Instances

Instances details
PMultiplicativeMonoid PInteger Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pone :: forall (s :: S). Term s PInteger Source #

ppowNatural :: forall (s :: S). Term s PInteger -> Term s PNatural -> Term s PInteger Source #

PMultiplicativeMonoid PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pone :: forall (s :: S). Term s PNatural Source #

ppowNatural :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

PMultiplicativeMonoid PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pone :: forall (s :: S). Term s PPositive Source #

ppowNatural :: forall (s :: S). Term s PPositive -> Term s PNatural -> Term s PPositive Source #

PMultiplicativeMonoid PRational Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Rational

Methods

pone :: forall (s :: S). Term s PRational Source #

ppowNatural :: forall (s :: S). Term s PRational -> Term s PNatural -> Term s PRational Source #

class (PAdditiveGroup a, PMultiplicativeMonoid a) => PRing (a :: S -> Type) where Source #

Laws

  1. pfromInteger 0 = pzero
  2. pfromInteger 1 = pone
  3. pfromInteger (x + y) = pfromInteger x #+ pfromInteger y
  4. pfromInteger (x * y) = pfromInteger x #* pfromInteger y

Additionally, the following 'interaction laws' must hold between the instances of PAdditiveGroup and PMultiplicativeMonoid for a:

  1. x #* (y #+ z) = (x #* y) #+ (x #* z) (#* left-distributes over #+)
  2. (y #+ z) #* x = (y #* x) #+ (z #* x) (#* right-distributes over #+)

Since: 1.10.0

Minimal complete definition

Nothing

Methods

pfromInteger :: forall (s :: S). Integer -> Term s a Source #

default pfromInteger :: forall (s :: S). PRing (PInner a) => Integer -> Term s a Source #

Instances

Instances details
PRing PInteger Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pfromInteger :: forall (s :: S). Integer -> Term s PInteger Source #

PRing PRational Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Rational

Methods

pfromInteger :: forall (s :: S). Integer -> Term s PRational Source #

class (PRing a, POrd a) => PIntegralDomain (a :: S -> Type) where Source #

Laws

Pedantry note

Technically, the requirements here are too strong: we demand an ordered ring, which integral domains don't necessarily have to be. However, in our case, our hand is forced by expected semantics: in abstract algebra, both the absolute value and the signum are real numbers (which are always totally ordered) but in our case, both must be elements of the integral domain itself. Thus, in order for the laws to make any sense, we have to ensure a total order on the integral domain. Since all of our integral domains are 'at least as big' as the integers, this doesn't pose a huge problem.

Since: 1.10.0

Minimal complete definition

Nothing

Methods

psignum :: forall (s :: S). Term s (a :--> a) Source #

default psignum :: forall (s :: S). Term s (a :--> a) Source #

pabs :: forall (s :: S). Term s (a :--> a) Source #

default pabs :: forall (s :: S). Term s (a :--> a) Source #

Instances

Instances details
PIntegralDomain PInteger Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

psignum :: forall (s :: S). Term s (PInteger :--> PInteger) Source #

pabs :: forall (s :: S). Term s (PInteger :--> PInteger) Source #

PIntegralDomain PRational Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Rational

Methods

psignum :: forall (s :: S). Term s (PRational :--> PRational) Source #

pabs :: forall (s :: S). Term s (PRational :--> PRational) Source #

Functions

positiveToInteger :: Positive -> Integer Source #

Since: 1.10.0

toPositiveAbs :: Integer -> Positive Source #

Converts negative Integers into their absolute values, positive Integers into their Positive equivalents. Errors on 0.

Since: 1.10.0

ptryPositive :: forall (s :: S). Term s (PInteger :--> PPositive) Source #

Partial version of ppositive. Errors if argument is not positive.

Since: 1.10.0

ppositive :: Term s (PInteger :--> PMaybe PPositive) Source #

Build a PPositive from a PInteger. Yields PNothing if argument is not positive.

ptryNatural :: forall (s :: S). Term s (PInteger :--> PNatural) Source #

Partial version of pnatural. Errors if argument is negative.

Since: 1.10.0

pnatural :: forall (s :: S). Term s (PInteger :--> PMaybe PNatural) Source #

Build a PNatural from a PInteger. Yields PNothing if given a negative value.

Since: 1.10.0

ppositiveToNatural :: forall (s :: S). Term s (PPositive :--> PNatural) Source #

'Relax' a PPositive to PNatural. This uses punsafeCoerce underneath, but because any positive is also a natural, is safe.

Since: 1.10.0

pnaturalToPositiveCPS :: forall (a :: S -> Type) (s :: S). Term s a -> (Term s PPositive -> Term s a) -> Term s PNatural -> Term s a Source #

Specialized form of pmaybe for PNatural. Given a default, and a way to turn a PPositive into an answer, produce the default when given pzero, and apply the function otherwise.

Since: 1.10.0

pbySquaringDefault :: forall (a :: S -> Type) (s :: S). (forall (s' :: S). Term s' a -> Term s' a -> Term s' a) -> Term s a -> Term s PPositive -> Term s a Source #

A default implementation of exponentiation-by-squaring with a strictly-positive exponent.

Important note

This implementation assumes that the operation argument is associative.

Since: 1.10.0

pdiv :: forall (s :: S). Term s (PInteger :--> (PInteger :--> PInteger)) Source #

Since: 1.10.0

pmod :: forall (s :: S). Term s (PInteger :--> (PInteger :--> PInteger)) Source #

Since: 1.10.0

pquot :: forall (s :: S). Term s (PInteger :--> (PInteger :--> PInteger)) Source #

Since: 1.10.0

prem :: forall (s :: S). Term s (PInteger :--> (PInteger :--> PInteger)) Source #

Since: 1.10.0

Orphan instances

PIntegralDomain a => Num (Term s a) Source # 
Instance details

Methods

(+) :: Term s a -> Term s a -> Term s a Source #

(-) :: Term s a -> Term s a -> Term s a Source #

(*) :: Term s a -> Term s a -> Term s a Source #

negate :: Term s a -> Term s a Source #

abs :: Term s a -> Term s a Source #

signum :: Term s a -> Term s a Source #

fromInteger :: Integer -> Term s a Source #